One of the most known techniques that every sudoku enthusiasts do is finding the naked and hidden singles/pairs in a sudoku puzzle. It is really important to understand exactly what they are and how they work to solve puzzles faster and more efficiently. So how does it work? Let me explain.
What are Naked Singles/Pairs?
Naked singles/pairs is a basic Sudoku technique that’s very easy to learn and use. A naked single is when you have exactly one exact candidate or number in exactly one cell within a row, column, or 3×3 block. The same rule with naked single applies to naked pairs, except you have two exact candidates in exactly two cells within a row, column, or 3×3 block. So for you to further understand naked singles/pairs, an example is shown below.
Image Credit : Sudoku9981
In naked singles/pairs using pencil marks will be very beneficial for you to find naked singles/pairs. The figure above is an example of naked singles. After listing all the possible candidates in every cell of the 3×3 block, you will notice that number 8 is only possible to appear in Row 2 Column 3 (R2C3) and R2C6. And from the definition of naked singles/pairs, then number 8 is definitely a naked single since they are the sole candidate in the said cell.
Moreover, the figure below is an example of naked pair. After looking at Row 8 and listing all the possible candidates in every cell in that row, numbers 2 and 6 can only be placed in R8C7 and R8C8. This means they are naked pair. With that, we can remove 2 and 6 in R8C4 since we are sure that they are in R8C7 and R8C8.
Image Credit : SudokuAcademy
What are Hidden Singles/Pairs?
The question now is how hidden singles/pairs differ from naked singles/pairs. Actually, the rules are both similar. Basically speaking, hidden single/pair exists when a single/pair of empty cells within a row, column or 3×3 block contains one (hidden single) or two (hidden pair) candidates that do not occur in any of the other empty cells of the region. A hidden pair differs from a naked pair in that there are more than 2 candidates for the pair, but only 2 are confined to the pair. A hidden pair allows us to eliminate all the other candidates from the empty cells of the pair. Hidden single/pair will be tougher to find compared to naked single/pair. It was called hidden because there are other candidates that hide the hidden single/pair.
Image Credit : sudoku.com
In the 3×3 block highlighted in blue from the picture above, the number is a hidden single. Why? Because any other cells within that block cannot have 1 after using pencil marks. It was called hidden single because, in that cell (R7C3), 1 was “hidden” by 7 and 8, or simply 1 was not the only plausible candidate initially. And for hidden pairs, the example below shows that numbers 2 and 5 in column 5 are considered hidden pairs. Again, 2 and 5 can only be seen in R2C5 and R6C5. They were just hidden by the other candidates in that cell.
Image Credit : sudoku Academy
Well, that’s it about naked and hidden singles/pairs. They are basically the same, with just a few differences. Don’t be too hard on yourself if you first find it hard to do. Just keep on practicing. Good luck!